In the previous article, we have seen how Determinant decides whether a system of equation (read square matrix) has inverse, or it has a solution, only when the determinant is not zero. The determinant is obtained from the equation given below.

To know more about finding determinant in this way , read previous article. Here we will discuss about finding determinant by cross multiplication but before that let us understand the different notations used to represent determinants.

### Notation For Determinants

There are several notation for determinants given by earlier mathematicians. Suppose represents a augmented matrix from a system of linear equations, then determinant of is given below.

```
Let the matrix be a 2 x 2 matrix.
Different ways to represent determinant of matrix -- (1)
-- (2)
-- (3)
```

### Determinant as a Function

Imagine determinant to a function that take a square matrix as input and give a single value as output. For example, be a function where could be any real number. Similarly, is a function that matrix as input and give a determinant value . The determinant value is always integer because it is linear combination of integers, that is, all values are integers in the matrix.

**Determinant of Matrix**

If is a matrix with just one element, then its determinant is the same element.

**Example #1**

```
Let be a square matrix of order
Then the determinant of is
```

### Determinant of Matrix

The determinant of a matrix is obtained by performing cross multiplication. See the following figure.

**Example #2**

Let be a square matrix. Find the determinant of the matrix .

**Solution:**

```
Let the be 2 x 2 square matrix.
```

**Example #3**

Let be a square matrix of order . Find the determinant of the matrix .

**Solution:**

```
Let be a square matrix of order .
```

### Determinant Of Matrix

The determinant of a matrix is also possible through cross multiplication; Since we have a larger matrix we need to convert the larger matrix into smaller matrix to compute determinant. See figure below.

The post Finding Determinant By Cross Multiplication appeared first on Notesformsc.